Journal ArticleDOI
Small semiovals in PG(2, q)
György Kiss,György Kiss +1 more
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TLDR
A semioval in a projective plane is a nonempty subset S of points with the property that for every point P ∈ S there exists a unique line l such that S \cap \le = \{P\}\) as mentioned in this paper.Abstract:
A semioval in a projective plane \(\prod\) is a nonempty subset S of points with the property that for every point P ∈ S there exists a unique line l such that \(S \cap \le = \{P\}\). It is known that \(q +1 \leq \|S\| \leq q\sqrt{q} + 1\) and both bounds are sharp. We say that S is a small semioval in \(\prod\) if \(\|S\| \leq 3(q + 1)\).read more
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On the spectrum of the sizes of semiovals in PG(2,q) , q odd
TL;DR: Some characterization theorems and non-existence results of semiovals with extra properties are proved and new examples of large Semiovals for q=11 and q=13 are constructed.
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On the Structure of Semiovals of Small Size
TL;DR: In this paper, the classification of all semi-ovals and blocking semiovals in PG(2, 8) is determined and new theoretical results on the structure of semi-vals containing a (q−1)-secant and some nonexistence results are presented.
Journal ArticleDOI
Semiarcs with a long secant in PG(2,q)
TL;DR: In this article, it was shown that if a small t-semiarc St in PG(2, q) has a large collinear subset K, then the tangents to St at the points of K can be blocked by t points not in K.
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Semiarcs with a long secant in $\mathrm{PG}(2,q)$
TL;DR: In this paper, it was shown that small semiarcs with large collinear subsets can be blocked by small points not in the subsets of the points in the semiarc.
On the minimum blocking semioval in PG(2,11)
TL;DR: A blocking semioval is a set of points in a projective plane that is both a blocking set (i.e., every line meets the set, but the set contains no line) and a semioval (e.g., there is a unique tangent line at each point) as mentioned in this paper .
References
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Journal ArticleDOI
Semiovals with large collinear subsets
TL;DR: In this paper, it was shown that no semioval can contain a full line, and that apart from two small cases, no semovals can contain all but one point of some line.
Journal ArticleDOI
Two Families of Blocking Semiovals
TL;DR: Two new families of blocking semiovals are constructed in desarguesian planes, motivated by Batten and Dover.